Graph of sine: F(x)=4-3sin(2x-2pi)

[Aladdin]

I'm a bit confused from a question wondering if my answer is true or not, which in some how will be easy for some .

F(x)=4-3sin(2x-2pi)

Calculate the center of symmetry,the axis of symmetry of F(x) in [pi,2pi].

 

[arthur ohlsten]

Re: Graph of sin

I find it easier to "see" a problem if I sketch the function.


1)sketch a x,y coordinate system.
2)on the y axis mark the x axis intercept 4.
3)along the x axis mark the axis 0, about 2 inch's to the right mark the axis pi, another 2 inch's to the right mark the axis 2pi

f[x]=4 - 3 sin[2x-2pi] pi<x<2pi
f[pi]=4-3sin[2pi-2pi]
f[pi]=4-3sin[0]
f[pi]=4
place a red dot on the x axis at pi

f[2pi]=4-3sin[2(2pi)-2pi]
f[2pi]=4-3sin 2pi
f[2pi=4
place a red dot on the x axis at x=2pi

1/2 way between at x= 5pi/4 place a red dot on the x axis. It is left as a exercize for the student to calculate this value

you can now sketch a inverted sin wave between x=pi and x=2pi with its minimum value of 1 at x=5 pi/4 and a maximum of 7 at x =7pi/4

please check for math errors

I don't believe there is a axis of symmetry, or center of symmetry , but check your text for the definition of these terms and determine for yourself the correct answer
Arthur

 

[Aladdin]

Re: Graph of sin

Thank you Arthur, but the question consist of two parts a) and b).

a) Let f(x)=4-3sin(2x-2pi)
Calculate the center of symmetry, the axis of symmetry of f(x) in [pi,2pi]
b)Draw the graph of f(x) in [pi,2pi].

I drew the graph , but I have to answer the first question first then the second isn't ?

 

[arthur ohlsten]

Re: Graph of sin

I can not answer the first part.
As I said in the answer, I don;t believe there is any axis of symmetry or center of symmetry for the function;s domain.
I am not sure of the definition of "symmetry", and I suggest you look in your text for the definition and then determine the axis, and center of symmetry
Arthur

 

[Aladdin]

Re: Graph of sin

I can not answer the first part.
As I said in the answer, I don;t believe there is any axis of symmetry or center of symmetry for the function;s domain.
I am not sure of the definition of "symmetry", and I suggest you look in your text for the definition and then determine the axis, and center of symmetry
Arthur

No , it's okay .

 

[fasteddie65]

Re: Graph of sin

Graphing it on a calculator, it looks like the point of symmetry is (3?/2, 4).

The axis of symmetry is y = 4.


Just my two cents.

 

[Aladdin]

Thank you